![Page 1: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/1.jpg)
Physics 2112
Unit 18
Today’s Concepts:A) Induction
B) RL Circuits
Electricity & Magnetism Lecture 18, Slide 1
![Page 2: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/2.jpg)
Where we are…..
Unit 17, Slide 2
Just finished
introducing
magnetism
Will now apply
magnetism to AC
circuits
![Page 3: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/3.jpg)
Remember Example 17.6 (solenoid)??
Unit 17, Slide 3
What if you only had the outer set of loops?
Would changing current in that induce anything?
1. Changing current in outer
set of loops
2. Caused changing magnetic
field in inner loops
3. Induced changing current in
inner loops.
![Page 4: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/4.jpg)
Self Inductance
Electricity & Magnetism Lecture 18, Slide 4
IL B
dt
dIL
dt
LId
dt
d B −=−=
−=)(
Define:
Depends only on the
geometry of the coils
Voltage drop in a coil
…caused by changes in the
current in that same coil
![Page 5: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/5.jpg)
L
What is the inductance of a long coil of wire (a solenoid)?
Example 18.1 (Inductance of Solenoid)
Electricity & Magnetism Lecture 18, Slide 5
![Page 6: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/6.jpg)
Increasing current
What the minus sign means…..
Electricity & Magnetism Lecture 18, Slide 7
dt
dIL−=
DV < 0VA > VB
A B
Acts like a resistor
IAB DVAB
zrnLB
22
0 =
volumen *2
0=
![Page 7: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/7.jpg)
decreasing current
What the minus sign means…..
Electricity & Magnetism Lecture 18, Slide 8
dt
dIL−=
DV > 0VA < VB
A B
Acts like a battery
IAB DVAB
However you try to change the current through an inductor, the inductor resists that change.
![Page 8: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/8.jpg)
current I
L
dIdt
L = −L
emf induced across L tries to keep I constant.
Inductors prevent discontinuous current changes!
It’s like inertia!
What this really means:
Electricity & Magnetism Lecture 18, Slide 9
Units of inductance are Henrys (H) [Tm2/A]
![Page 9: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/9.jpg)
RL
VBATT
I = 0
Time Constant
Electricity & Magnetism Lecture 18, Slide 10
R
L=
)1( /teR
VI −−=
![Page 10: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/10.jpg)
R=120WL
12V= VBATT
S
Example 18.2 (Current in Solenoid)
Electricity & Magnetism Lecture 18, Slide 11
R
L=)1( /te
R
VI −−=
A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120W resistor and a 12V battery.
What is the current through the resistor 0.01sec after the switch is closed?
What is the current through the resistor 2.0 sec after the switch is closed?
Would the current have been at 0.01sec if the inductor had an internal resistance of 20W?
![Page 11: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/11.jpg)
RL
At t = 0:I = 0
VL = VBATT
VR = 0
(L is like a giant resistor)
VBATT
I = 0
At t >> L/R:
VL = 0
VR = VBATT
I = VBATT/R
(L is like a short circuit)
R
I = V/R
L
VBATT
When no current is flowing initially:
How to think about RL circuits:
Electricity & Magnetism Lecture 18, Slide 12
VL
R
L=
I
![Page 12: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/12.jpg)
What is the current I through the vertical resistor immediately after the switch is closed? (+ is in the direction of the arrow)
A) I = V/R
B) I = V/2R
C) I = 0
D) I = −V/2R
E) I = −V/R
In the circuit, the switch has been open for a long time, and the current is zero everywhere.
At time t = 0 the switch is closed.
I
I
CheckPoint 2A
Electricity & Magnetism Lecture 18, Slide 13
![Page 13: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/13.jpg)
What is the current I through the vertical resistor immediately after the switch is closed?
(+ is in the direction of the arrow)
A) I = V/R
B) I = V/2R
C) I = 0
D) I = −V/2R
E) I = −V/RI
I
Confusion about question….
Electricity & Magnetism Lecture 18, Slide 14
C) there is no current at t=0
I mean a little “dt” of time after t=0
![Page 14: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/14.jpg)
What is the current I through the vertical resistor immediately after the switch is opened?
(+ is in the direction of the arrow)
A) I = V/R
B) I = V/2R
C) I = 0
D) I = −V/2R
E) I = −V/R
After a long time, the switch is opened, abruptly disconnecting the battery from the circuit.
CheckPoint 2B
Electricity & Magnetism Lecture 18, Slide 15
![Page 15: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/15.jpg)
RL
VBATT
I = V/R
At t >> L/R:
I = 0
VL = 0
VR = 0
R
I = 0
LR
I = VBATT/R
VR = IR
VL = VR
At t = 0:
When steady current is flowing initially:
How to Think about RL Circuits Episode 2:
VL
R
L=
R
L=
Electricity & Magnetism Lecture 18, Slide 16
![Page 16: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/16.jpg)
R
I
V = IRdIdt
V = L L
+
−
−
+
Why is there Exponential Behavior?
VL
R
L=
R
L=
Electricity & Magnetism Lecture 18, Slide 17
0=+ IRdt
dIL
whereR
L=
/0
/
0)( tLtR eIeItI −− ==
![Page 17: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/17.jpg)
Prelecture:
RL
I
Lecture:
VL
VBATT
Did we mess up?
No: The resistance is simply twice as big in one case.
R
L=
Electricity & Magnetism Lecture 18, Slide 18
Quick comment…
![Page 18: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/18.jpg)
Inside your i-clicker
” Can you have capacitors and inductors in the same circuit?“why inductors are important as opposed to capacitors. why use one instead of the other?”
What are Inductors and Capacitors Good For?
Electricity & Magnetism Lecture 18, Slide 19
![Page 19: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/19.jpg)
After long time at 0, moved to 1 After long time at 0, moved to 2
After switch moved, which case has larger time constant?
A) Case 1B) Case 2C) The same
CheckPoint 3A
Electricity & Magnetism Lecture 18, Slide 20
![Page 20: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/20.jpg)
After long time at 0, moved to 1 After long time at 0, moved to 2
After switch moved, which case has larger time constant?
A) Case 1B) Case 2C) The same
R
L
21 =
R
L
32 =
CheckPoint 3A
Electricity & Magnetism Lecture 18, Slide 21
![Page 21: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/21.jpg)
A) Case 1B) Case 2C) The same
CheckPoint 3B
Electricity & Magnetism Lecture 18, Slide 22
After long time at 0, moved to 1 After long time at 0, moved to 2
Immediately after switch moved, in which case is the voltage across the inductor larger?
![Page 22: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/22.jpg)
A) Case 1B) Case 2C) The same
Before switch moved: R
VI =
After switch moved:
RR
VVL 21 =
RR
VVL 32 =
CheckPoint 3B
Electricity & Magnetism Lecture 18, Slide 23
After long time at 0, moved to 1 After long time at 0, moved to 2
Immediately after switch moved, in which case is the voltage across the inductor larger?
![Page 23: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/23.jpg)
A) Case 1B) Case 2C) The same
CheckPoint 3C
Electricity & Magnetism Lecture 18, Slide 25
After long time at 0, moved to 1 After long time at 0, moved to 2
After switch moved for finite time, in which case is the current through the inductor larger?
![Page 24: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/24.jpg)
A) Case 1B) Case 2C) The same
Immediately after: 21 II =
After awhile
1/
1t
IeI−
=
2/
2t
IeI−
=
21 >
CheckPoint 3C
Electricity & Magnetism Lecture 18, Slide 26
After long time at 0, moved to 1 After long time at 0, moved to 2
After switch moved for finite time, in which case is the current through the inductor larger?
![Page 25: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/25.jpg)
Energy Stored
Unit 18, Slide 27
VIdt
energydPower ==
)(
2
2
1LIEstored =
2
2
1
C
QEstored =
For inductor Recall for capacitor
Energy stored in
the magnetic field
Energy stored in
the electric field
![Page 26: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/26.jpg)
R=100WL
12V= VBATT
S
Example 18.3 (Energy in Solenoid)
Electricity & Magnetism Lecture 18, Slide 28
A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120W resistor and a 12V battery.
What is the energy stored in the inductor 0.01sec after the switch is closed?
What is the energy stored in the inductor 2.0 sec after the switch is closed?
2
2
1LIEstored =
![Page 27: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/27.jpg)
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the open position for a long
time in the circuit drawn above. What is the total
current out of the battery, Itot, immediately after the
switch is closed? (The inductor is “ideal”.)
Question
![Page 28: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/28.jpg)
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the open position for a long
time in the circuit drawn above. What is the current
across the resistor, I1, immediately after the switch
is closed? (The inductor is “ideal”.)
Question
![Page 29: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/29.jpg)
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120
V
The switch has been in the open position for a long
time in the circuit drawn above. What is the current
across the inductor, I2, immediately after the switch
is closed? (The inductor is “ideal”.)
Question
![Page 30: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/30.jpg)
A. 0V
B. 80V
C. 90V
D. 120V
E. 240V
120
V
The switch has been in the open position for a long
time in the circuit drawn above. What is the voltage
drop across the inductor immediately after the
switch is closed? (The inductor is “ideal”.)
Question
![Page 31: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/31.jpg)
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
current across the inductor, I2? (The inductor is
“ideal”.)
Question
![Page 32: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/32.jpg)
A. 0V
B. 80V
C. 90V
D. 120V
E. 240V
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
voltage difference across the inductor immediately
after the switch is opened? (The inductor is “ideal”.)
Question
![Page 33: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/33.jpg)
A. 0A
B. 4A
C. 6A
D. 12A
E. -4A
120V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
current across the inductor, I2 immediately after the
switch is open? (The inductor is “ideal”.)
Question
![Page 34: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/34.jpg)
A. 6A/sec
B. 80A/sec
C. 90A/sec
D. 120A/sec
E. 240A/sec
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. What is the
rate change for the current through the inductor
immediately after the switch is opened? (The
inductor is “ideal”.)
Question
![Page 35: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/35.jpg)
A. VA > VB
B. VA = VB
C. VA < VB
120
V
The switch has been in the open position for a long
time in the circuit drawn above. Which point has a
higher electrical potential immediately after the
switch is closed? (The inductor is “ideal”.)
Question
A
B
![Page 36: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/36.jpg)
A. VA > VB
B. VA = VB
C. VA < VB
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. Which point
has a higher electrical potential? (The inductor is
“ideal”.)
Question
A
B
![Page 37: Physics 2112 Unit 18 - College of DuPage · 2020. 4. 1. · Electricity & Magnetism Lecture 18, Slide 28 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached](https://reader034.vdocument.in/reader034/viewer/2022051917/600964009213a75b9224d3e6/html5/thumbnails/37.jpg)
A. VA > VB
B. VA = VB
C. VA < VB
120
V
The switch has been in the closed position for a
long time in the circuit drawn above. Which point
has a higher electrical potential immediately after
the switch is opened? (The inductor is “ideal”.)
Question
A
B